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We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study amenability of these groups. This is a draft of a paper which will be extended by some other results.arXiv:1412.6657v1 fatcat:dolv2cwy5vfzddojl2d6tzogtq